Information on Result #1523260
Linear OOA(3131, 2820, F3, 3, 25) (dual of [(2820, 3), 8329, 26]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3131, 2820, F3, 2, 25) (dual of [(2820, 2), 5509, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3131, 3286, F3, 2, 25) (dual of [(3286, 2), 6441, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3131, 6572, F3, 25) (dual of [6572, 6441, 26]-code), using
- construction XX applied to Ce(24) ⊂ Ce(22) ⊂ Ce(21) [i] based on
- linear OA(3129, 6561, F3, 25) (dual of [6561, 6432, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3121, 6561, F3, 23) (dual of [6561, 6440, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3113, 6561, F3, 22) (dual of [6561, 6448, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(24) ⊂ Ce(22) ⊂ Ce(21) [i] based on
- OOA 2-folding [i] based on linear OA(3131, 6572, F3, 25) (dual of [6572, 6441, 26]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3131, 1410, F3, 5, 25) (dual of [(1410, 5), 6919, 26]-NRT-code) | [i] | OOA Folding | |